The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• The Total Position-Spread (TPS) tensor is a key observable in quantum systems.
• Understanding its behavior in one-dimensional Heisenberg chains is crucial for characterizing magnetic properties.

Purpose of the Study:

• To investigate the spin partition of the TPS tensor in one-dimensional Heisenberg chains.
• To correlate the behavior of the spin-partitioned TPS (SP-TPS) tensor with the presence or absence of energy gaps.

Main Methods:

• Performed spin partition of the TPS tensor for Heisenberg chains with open boundary conditions.
• Considered both ferromagnetic (high-spin) and anti-ferromagnetic (low-spin) ground states.
• Analyzed the effect of alternating magnetic couplings on spin-pairing in low-spin states.

Main Results:

• The SP-TPS tensor's growth with the number of sites is linked to the energy gap.
• A gapped energy spectrum corresponds to linear growth of the SP-TPS tensor.
• Gapless systems exhibit faster-than-linear growth, leading to divergence of the per-site SP-TPS value.
• Derived an analytical expression for SP-TPS dependence on system size and total spin projection for high-spin states.

Conclusions:

• The SP-TPS tensor serves as an indicator of the energy gap in one-dimensional Heisenberg chains.
• The study provides insights into the relationship between spin correlations, system size, and spectral properties.